A bioreactor can be defined as a system in which a biological conversion is effected. This definition can apply to any conversion involving enzymes, micro-organisms, or animal, insect or plant cells. Artworkers sometimes distinguish between a bioreactor and a fermentor since in the strictest sense a fermentor is a system that provides an anaerobic process for producing alcohol from sugar. The dichotomy in nomenclature is most often used to distinguish between animal and bacterial cell culture despite the fact that a bioreactor and a fermentor are generally similar in design. However, we will use the word bioreactor in a generic sense to refer to any type of container (usually made of glass, metal or polymer) in which organisms including microbes, animal, insect or plant cells and bacteria (all being hereinafter referred to generally as “cells”) are cultivated in a controlled manner. Therefore, unless otherwise indicated, the term bioreactor will be considered as including a fermentor.
The goal of an effective bioreactor is to contain, control, and positively influence a particular desired biological reaction. One desired biological reaction considered here is the growth of unicellular microorganisms. The most popular method for accomplishing this is a batch cultivation system. See, for example, James Lee, Biochemical Engineering, Washington State University, e-book, 2002. For simplicity and clarity we will describe in detail here a batch process, although the analytical apparatus and methods described and claimed herein apply also to continuous growth processes (e.g.: perfusion). In a batch method, the microorganisms are inoculated into the culture medium and the growth cycle then commences. This growth cycle comprises the following phases:    1. Lag phase: A period of time during which the cells have not yet commenced growth    2. Accelerated growth phase: The period during which the number of cells increases and the cell division rate reaches a maximum.    3. Exponential growth phase: The period during which the number of cells increases exponentially as the cells divide. The growth rate (cell concentration) is increasing during this phase, although the cell division rate is substantially constant and at its maximum.    4. Decelerated growth phase: After the growth rate has reached a maximum it is followed by a deceleration in both the growth rate and cell division rate.    5. Stationary phase: The cell population reaches a maximum value and thereafter does not significantly increase.    6. Death phase: After nutrients available to the cells are depleted and/or the bioreactor environment becomes too hostile, cells will start to die and the number of viable cells will decrease.
These stages are graphically illustrated in FIG. 1 which shows the change in measured cell density (concentration) vs. time for a typical bioprocess with each of the six phases indicated.
In order to optimize the growth process, it is beneficial to monitor the growth process by observing the change in cell density during each of the six phases described above. In particular, it is desirable to achieve maximum yield by harvesting the cells at stage 5, or as close thereto as possible, i.e., when the maximum number of viable cells is present in the bioreactor growth medium. In the past, the monitoring of cell density was done off-line. Off-line here means not being in real time, and is conventionally done by taking a sample out of the bioreactor for examination. The examination is often accomplished either by drying and then weighing the dried sample or by diluting the drawn sample and placing the diluted sample in a spectrophotometer. The dry cell weight is generally considered the most accurate method, but it often takes 7-10 days to obtain the results. This time lag renders it impossible to effect any change in reaction conditions in the run under study; and obviously control loops can not be implemented. Another prior art, off-line method using a spectrophotometer is often called an optical density measurement. This optical method is common but is also not a true real time measurement and has accuracy issues associated with its implementation, specifically the need to highly dilute the sample removed from the bioreactor so that its optical loss is within the dynamic operating range of the spectrophotometer.
Due to the time, effort, and lack of availability of real time information with the aforementioned off-line cell density measurement methods, many attempts to automate this measurement and make it real time have been made. Recently, so called turbidity probes have been employed to give a measurement which can be related to the cell density in a bioreactor. A picture of a typical prior art turbidity probe used for this application is shown schematically in FIG. 2. In this device a light source 2 is used to illuminate a gap 4 in which the cell containing, bioreactor liquid under study is located. The light traverses the gap, and that portion of the light that is not scattered or absorbed by the liquid is incident upon the detector 5 and gives a signal. It is desirable that a strong linear correlation exist between the cell concentration in the medium in the gap, and the signal arriving at the detector. Electronics and firmware are sometimes configured such that a baseline reading in a neutral fluid (e.g.: de-ionized water) is used for comparison. However, the resulting measurements are often not as linear or strongly correlated to cell density as is necessary. The reasons for this discrepancy and a solution in accordance with the present invention are discussed below.
Many of the turbidity meters currently used in the biotech area have their heritage in turbidity measurements for wastewater characterization. The commonly used definition of turbidity also has its origin in the wastewater industry and is, “Turbidity, an expression of the optical properties of a liquid that causes light rays to be scattered and absorbed rather than transmitted in straight lines through a sample” [see ASTM Standard Test Method for Turbidity in Water, D 1889-00, ASTM International, 2002)] In general, this is not a specific enough description of the physical phenomenon to permit a concise mathematical definition. Without a precise mathematical definition, it is difficult to define and construct a precise and repeatable measuring method or instrument. This problem is one reason why the United States EPA has apparently experienced difficulty in getting the various vendors of turbidity meters to agree with each other on a measurement standard. Unfortunately, all of the turbidity meters currently being used to give measurements proportional to cell density are limited in at least one of several essential ways. The limitations frequently stem from the use of incoherent, broad bandwidth light sources such as lamps and LEDs, and/or large optical beams and large field of view detectors. These limitations manifest themselves in the way the probe respond to a bioreactor medium in which significant scattering occurs and can frequently therefore lead to ambiguous results. An additional ambiguity results from the fact that the size and refractive index of the bioparticle (cell) will frequently change during the course of the cell growth process.
Also, part of this ambiguity is due to the fact that scattering phenomena are inherently difficult to describe precisely [see Akira Ishimaru, Wave Propagation and Scattering in Random Media, IEEE Press 1997]. For example, scattering does not strictly follow Beer's law, which holds rigorously only for absorbing solutions and even then only up to the point where the concentration of the solute becomes sufficiently high that electrostatic interactions occur which actually change the solute's absorptive properties. In a scattering medium, Beer's law will generally only hold up to around 1 AU of loss where loss in AU is defined as:
                    Loss        =                  Absorbance          ≡                                                    Log                10                            ⁡                              [                                                      I                    t                                                        I                    0                                                  ]                                      ⁢            AU                                              Eq        .                                  ⁢        1            where It/I0 is the ratio of the transmitted intensity to the initial intensity. It should be noted that the use of the units AU or absorption units is somewhat of a misnomer for scattering systems. Although the language and machinery of Beer's law is based on absorptive loss, turbidity probes for cell density measurement nevertheless generally give their results in AU; although occasionally turbidity units NTU (nephelometric turbidity units) or JTU (Jackson turbidity units) are employed. It should also be noted that off-line cell density measurement using a spectrophotometer owes its accuracy problems in part to the fact that the samples drawn from a bioreactor need to be significantly diluted in order to allow the spectrophotometer to operate in a regime where it sees less than 1 AU of loss.
Herein when we refer to Beer's law, we refer specifically to the exponential decay of light intensity as a function of distance or with the concentration of a target analyte dispersed in a medium. This can be expressed mathematically as:I(x)/I(0)=It/I0=e−ξx  Eq. 2
Here ξ is the combined loss coefficient due to both scattering and absorption, x is the distance the optical beam has propagated into the sample, and It/I0 is the ratio of the transmitted intensity to the initial intensity where It represents the intensity transmitted through the medium from the origin to point x, and e is the base constant of the natural logarithm=2.71828183. This type of behavior is shown in FIG. 3 where, for ease of illustration, the exponent has been defined as unity.
Very often the base 10 logarithm of both sides of Equation 1 is used and a linear relationship is thereby established between the incident and transmitted light intensity. This linear relationship, which defines the absorbance A, is shown in Equation 3:
                              A          ⁡                      (                          λ              ,              c                        )                          =                                            Log              10                        ⁡                          [                                                I                  t                                                  I                  0                                            ]                                =                      k            ⁢                                                  ⁢            ξ            ⁢                                                  ⁢            L                                              Eq        .                                  ⁢        3            
Here k is the base 10 logarithm of e. This linear relationship between absorbance, A, and loss coefficient ξ, or distance L in the x direction is a linear representation of Beer's Law. This depiction is sometimes useful because of the inherent simplicity of a straight line. An example is show in FIG. 4 for the measurement of absorbance in AU of Copper Sulfate (CuSO4) at 830 nm over a fixed distance with increasing concentration of CuSO4 
It has been noted many times and in many disciplines that Beer's law does not rigorously hold for scattering systems. This is often referred to as the “breakdown” of Beer's law. In fact, Beer's law does not break down, but rather only the assumptions under which it is applied. Generally, Beer's law is employed to describe the absorptive attenuation of an optical signal as a function of distance in the medium or as a function of concentration of the absorbing specie or species in the medium. However, Beer's law can also be used to describe the decay of light transmitted from the light source to a detector across a gap containing an absorbing or absorbing and weakly scattering medium.
If one assumes a perfectly collimated optical beam with a cross-sectional area that is no greater than the area of the detector and a purely absorptive medium between the source and the detector, then the only light that reaches the detector is the light that is not absorbed. However, one normally does not have a perfectly collimated optical beam, and in many existing cell density probes, the spatial extent of the beam exceeds the area of the detector. By recording the signal on the detector when a neutral (minimally absorbing, non-scattering) fluid like de-ionized water is present in the gap, it is possible to consider only the light that is actually hitting (impinging on) the detector. However, in a highly scattering (turbid) medium the situation is different irrespective of whether the beam is perfectly collimated and sized or not. Some portion of the light still makes it directly to the detector, but some light is singly scattered into the detector's field of view, and other light is multiply scattered and thereby also ends up in the detector's field of view. It is this scattering of light into the detector (specifically the light that would otherwise miss the detector in the absence of scattering) which causes deviations from what is predicted by Beer's law. Since most currently existing turbidity meters generally utilize a wide, divergent, incoherent optical beam there are many paths the source light can take into the detector. This is depicted in FIG. 5 in which the numbered components are as follows:    6. The optical source    7. A ray that misses the detector    8. The collimated rays that hit the detector    9. A scattering particle    10. A ray that would have missed the detector if it were not singly scattered into the detector    11. A ray that might have missed the detector but is multiply scattered into the detector    12. The detector    13. A collimated ray that would miss the detector if it were not scattered
Standard turbidity meters therefore do not accurately follow Beer's Law, and therefore are unable to provide a linear response in absorbance as a function of scattering density beyond ˜1 AU. Many fermentation runs and mammalian cell bioreactor growth runs will result in a medium that has an optical loss significantly exceeding 1 AU. This is often troublesome to the end user in the biotechnology arena who is accustomed to the linear response of other bioreactor analytical devices such as electrochemical pH and dissolved oxygen probes. The resulting nonlinear response of the cell density probe must be separated from the actual growth behavior of the cell specimens under study. Equally significant complications arise from the fact that the dynamic range of existing cell density probe is limited by its saturating response. As shown in FIG. 6, the response of a typical probe as a function of increasing density of scatterers (in this example ˜2 micron polystyrene micro-spheres) is that it saturates. At some point the slope of the response will approach zero. However, even before the slope reaches zero, a point will frequently be reached where any noise added to the signal will result in a loss of accurate information.
Additionally, it should be noted that the scattering pattern (behavior) of a particle depends heavily on the ratio of the wavelength (λ) of the incident light to the circumference of the particle [see H. C. van de Hulst, Light Scattering by Small Particles, Dover 1981]. Generally speaking, there exist 3 domains of interest from a scattering perspective:                Rayleigh Regime: d<<λ        Mie Regime: d ˜λ        Geometrical Optics Regime: d>>λwith d being the mean particle diameter. In the Rayleigh regime the scattering resembles dipole scattering, while in the Mie regime the scattering has a characteristic forward scattering behavior. The larger the diameter of the scatterer for a given wavelength of incident light, the more light is forward scattered. In the regime where the size of the particle is more than about two orders of magnitude larger than the optical wavelength, the scattering takes on the behavior of ray optics. Typical scattering patterns for Rayleigh and Mie scattering with various sizes of particles are shown in FIG. 7.        
I have found that the preferred optimal illumination wavelength for an optical loss probe in accordance with the present invention will be in the near infrared, preferably between 810 and 850 nm and most preferably about 830 nm. At about 830 nm water has its absorption minimum, which means that this wavelength is optimal for a probe that is to measure the decrease in transmissivity by biological material that is present in an aqueous medium, as is normally used for bioprocesses. Light at other wavelengths where there is absorption by the cells can, in principle, be used, but this adds ambiguity to the measurement. Even if the baseline absorption by the medium is accounted for, the mean free scattering path length will change as a function of scattering density, thereby adding uncertainty. Near the water absorption minimum at a wavelength of around 830 nm and given the size of the biological scatterers of interest (e.g.: mammalian cells, microbes), I have concluded that the scattering will be predominantly in the Mie scattering regime. It is important to remember that the magnitude of light scattered forward, as opposed to backwards or to the side, depends on the ratio of the light wavelength to scatterer diameter. As previously mentioned, the larger the scatterer relative to the wavelength, the larger the percentage of the incident light that is scattered forward. This means that for a given wavelength, the scattering density at which the probe's results will deviate from Beer's law will depend on the size of the scatterer. Given this fact, it is clear that the point at which a probe's loss saturates, or is sensitive to noise affecting the measurement, is a variable and will depend on factors including the size of the scatterer which is being measured. This is generally not a preferred situation, and in order to improve upon measurement accuracy, it is necessary to understand the underlying reasons for this variability. These underlying reasons will now be reviewed.
When determining if an analytical technique and/or instrument is suitable for use in monitoring a bioprocess, although it is instructive as a benchmark it is not essential to measure either the absolute concentration of cells or their precise size. The size range of a given cell line is generally known, although it can change during the course of the cell growth process. What is really important is to be able to determine, on a real time basis whether or not the bioprocess is proceeding in accordance with a known growth pattern. To achieve this the bioprocess engineer will seek to monitor cell density (concentration) vs. time or another parameter proportional to cell density. Many process development laboratories utilize a spectrophotometer and the resulting optical density (OD) measurement as a substitute for, or in addition to, manual or automated cell counting in order to monitor the growth process. The point of the invention described herein is to provide a functionally equivalent measurement, but one which is in-line, in real-time, and which manifests a linear response over a broad range of cell density. Existing spectroscopic measurements are incapable of achieving this result. In order to get a quantitative understanding of the cell growth process the user can correlate the optical loss measurement provided by the present invention with total cell density as measured using an automated cell counter such as those offered by Nova or Innovatis (e.g.: The Nova Flex or Nova 400 series (http://www.novabiomedical.com/biotechnology.html) or the Cedex by Innovatis (http://www.innovatis.com/)) by taking off-line samples and noting the results and time of sample. The user can also take samples and perform a dry cell weight measurement, or perform a manual cell count. The important fact is that these quantitative measurements are taken off-line and correlated to an optical loss measurement taken at-line at the same time in accordance with the present invention. A mathematical mapping between the optical loss measurement and the quantitative measurement used as a process variable can then be created and displayed. The apparatus of the present invention does not (and need not) directly measure a size or number density quantity of the cells in the bioreactor. The scattering based optical loss measured in accordance with the present invention does, however, correlate well to a function of mean scattering particle diameter, mean number density, and mean index of refraction. The technique and apparatus of the present invention permit this comparison with a high degree of accuracy and reliability. In other words, my invention provides a means to accurately monitor the course of a bioprocess and confirm whether or not it is proceeding in accordance with FIG. 1.
The prior art, as exemplified by U.S. Pat. No. 6,219,138, teaches a technique for confirming or determining particle size using a single illumination source (or multiple sources if the particle size is unknown). Although there is some similarity between the apparatus described in this patent and that of the present invention, the measurement objectives and results are certainly different and critical aspects of the apparatus of the present invention are likewise different. For example, the present invention always utilizes a single wavelength illumination source (i.e., not broadband), and does not measure (or need to precisely know) the size of the bioparticle, but rather accurately monitors the scattering loss of the reaction media over time i.e., during the course of the bioprocess. As indicated, it operates on the basis of an assumed maximum particle size which will generally be known with sufficient accuracy based on the particular cell being grown, and thereby permits an accurate monitoring of the status of a bioprocess. Additional differences between the product and process of the present invention and those of the prior art include the specific wavelength being chosen (810-850 nm, especially ˜830 nm) to be at a minimum of water absorption, and the use of a phase sensitive detection system.